Senator Keneally, Labor's spokeswoman for Home Affairs, said the Australian Border Force had on Wednesday afternoon confirmed she could visit the family.
But she said 22 minutes later she received an email saying Defence Minister Peter Dutton had "determined that the Special Purpose Aircraft can no longer be made available" for the trip.
"Dutton cancelled the trip," Senator Keneally wrote on Twitter on Wednesday night.
The Biloela family of Priya, Nades and their Australian-born daughters Kopika and Tharunicaa have spent more than three years in detention.
Community members have campaigned tirelessly for them to be returned to their adopted home in central Queensland.
Senator Keneally has said the "sorry saga" should come to an end, with taxpayers spending millions of dollars to keep the family in detention.
She had been due to visit Christmas Island with other MPs as part of a bipartisan parliamentary committee trip and she was planning on bringing a gift for the children, the ABC reports.
Mr Dutton's office has been sought for comment.
We'll chat with Kristina Keneally tonight on The Project at 6.30pm on Network 10.